The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A328181 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A328181

a(n) = (-1)^(bigomega(n) - omega(n)) * Sum_{d|n} (-1)^(bigomega(d) - omega(d)) * d.
(history; published version)

#15 by Joerg Arndt at Sun Nov 06 03:16:45 EST 2022

STATUS

reviewed

approved

#14 by Michel Marcus at Sun Nov 06 02:16:25 EST 2022

STATUS

proposed

reviewed

#13 by Amiram Eldar at Sun Nov 06 01:42:22 EST 2022

STATUS

editing

proposed

#12 by Amiram Eldar at Sun Nov 06 01:05:29 EST 2022

FORMULA

Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/30) * Product_{p prime} (1 + 2/p^2 - 2/p^3) = 0.5507877576... . - Amiram Eldar, Nov 06 2022

STATUS

approved

editing

#11 by Bruno Berselli at Wed Dec 02 03:15:50 EST 2020

STATUS

proposed

approved

#10 by Amiram Eldar at Wed Dec 02 02:18:49 EST 2020

STATUS

editing

proposed

#9 by Amiram Eldar at Wed Dec 02 02:05:19 EST 2020

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>.

FORMULA

Multiplicative with a(p^e) = (p^(e+1) - (-1)^e*(2*p+1))/(p+1). - Amiram Eldar, Dec 02 2020

MATHEMATICA

f[p_, e_] := (p^(e+1) - (-1)^e *(2*p+1))/(p+1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Dec 02 2020 *)

#8 by Amiram Eldar at Wed Dec 02 02:04:01 EST 2020

LINKS

Amiram Eldar, <a href="/A328181/b328181.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#7 by Vaclav Kotesovec at Mon Oct 07 11:01:56 EDT 2019

STATUS

editing

approved

#6 by Vaclav Kotesovec at Mon Oct 07 11:01:47 EDT 2019

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>

STATUS

proposed

editing